Problem: A group of adults and kids went to see a movie. Tickets cost $$8.00$ each for adults and $$2.50$ each for kids, and the group paid $$52.00$ in total. There were $4$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Explanation: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${8x+2.5y = 52}$ ${x = y-4}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-4}$ for $x$ in the first equation. ${8}{(y-4)}{+ 2.5y = 52}$ Simplify and solve for $y$ $ 8y-32 + 2.5y = 52 $ $ 10.5y-32 = 52 $ $ 10.5y = 84 $ $ y = \dfrac{84}{10.5} $ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into ${x = y-4}$ to find $x$ ${x = }{(8)}{ - 4}$ ${x = 4}$ You can also plug ${y = 8}$ into ${8x+2.5y = 52}$ and get the same answer for $x$ ${8x + 2.5}{(8)}{= 52}$ ${x = 4}$ There were $4$ adults and $8$ kids.